Technological innovations enable privacy in payments, but pose a fundamental conflict between freedom and control. We study the design of privacy-enhanced payment systems with regards to identity and transaction privacy. In our model, privacy is valued by users making legitimate transactions, but can be exploited by malicious actors for illicit financial activities with technologies that obfuscate their illicit nature. When these technologies are fixed, the optimal design can be complex in the sense that transaction privacy is provided to disjoint intervals of payment volume tailored around the technologies. However, when unlawful users can innovate their technologies, the optimal robust design is characterized by two simple features: an identity requirement and transaction privacy up to a threshold of payment volume. Our framework can be applied to compare a variety of payment systems, from legacy payment systems to public blockchains and crypto tumblers, based on their privacy features and enforcement capabilities; we draw policy implications regarding payment system regulation and the design of central bank digital currencies.

Blockchain represents a database technology that allows a group of self-interested users to maintain a distributed ledger without trusted party such as a bank. In this paper, we develop a new, game-theoretic formulation of any blockchain where each user decides how to update the distributed ledger. Blockchains are useful only in so far as the updating strategies of users attain consensus, that is, users agree on which version of the ledger is ``correct'' and do not have incentives to omit or modify past data. We show currently-implemented strategies---the longest chain rule---do not achieve consensus when users are sufficiently heterogeneous. We go on to prove existence of new equilibrium strategies that are mild modifications of the longest chain rule and attain consensus for any degree of heterogeneity. In practice, these equilibrium strategies are robust to so-called double-spending or 51% attacks.

Stablecoins are at the center of debate surrounding decentralized finance. We develop a dynamic model to analyze the instability mechanism of stablecoins, the complex incentives of stablecoin issuers, and regulatory proposals. The model rationalizes a variety of stablecoin management strategies commonly observed in practice, and we characterize an instability trap: stability can last for a long time, but once debasement happens, price volatility persists. Capital requirement improves price stability but fails to eliminate debasement. Restricting the riskiness of reserve assets can surprisingly destabilize price. Finally, data privacy regulation has an unintended benefit of reducing the price volatility of stablecoins issued by data-driven platforms.